This paper aims to significantly improve the efficiency of Mamdani Generalized Type-3 Fuzzy Systems, through the implementation of numerical methods, specifically Newton-Cotes integrators for achieving β-planes aggregation. The idea is reducing the number of β-planes needed to achieve the required fidelity with respect to the theoretical model. This requirement can vary depending on the application, however, enhancing the efficiency of the fuzzy system at the end reduces the computational effort of these systems, independently of the desired number of β-planes. The work includes the theoretical explanation and tests to determine the effectiveness of the proposal; the performance results are significantly better than the conventional approach (that corresponds to using a zero-order integrator) and the limitations and potential of the proposal are also explored in this paper.
Ontiveros et al. (Tue,) studied this question.